Optimization of the regime of shortening of relativistically strong laser pulses in the process of excitation of a plasma wake wave

A detailed theoretical investigation is performed for the self-compression of relativistically strong laser pulses under plasma wake wave excitation conditions. An analytical expression is obtained for the characteristic length of laser pulse self-compression in the one-dimensional case. A good agreement between the theoretical and numerical calculation of the dependence of the wave-packet compression length on both amplitude and plasma concentration is demonstrated. The influence of the wave beam self-focusing radiation process on the rate of shortening of the laser pulse duration is considered.

Figure 1

(a) Dynamics of laser pulse intensity under the conditions of plasma wake wave excitation. The initial parameters of the laser pulse are $a_0=1.25,{\tau }_p^{\mathrm{in}}=11T_0$, and ${({\omega }_p/{\omega }_0)}^2=2\times {10}^{-3}$, where $T_0$ is the period of the optical field. The duration of the compressed laser pulse at $z=57.5$ is ${\tau }_p^{\mathrm{out}}=1.32T_0$. The inset shows intensity distributions at $z=0$ and $z=57.5$. (b) Dynamics of laser pulse intensity (red solid curve) and plasma wave potential (blue dashed curve). Here, the intensity is always normalized to the maximum value.

Figure 2

Dynamics of laser pulse intensity under the conditions of plasma wake wave excitation for three different values of plasma density: (a) $n_e=2\times {10}^{18}$, (b) $n_e=4\times {10}^{18}$, (c) $n_e=6\times {10}^{18}$. The initial parameters of the laser pulse are $a_0=1.5$ and ${\tau }_p^{\mathrm{in}}=11T_0$. (d) presents the curve for laser pulse duration ${\tau }_{\mathrm{pulse}}$ calculated using the second-order moment for three values of plasma density. The arrows mark the positions of $L_c$, where the $z$ derivative of the wave-packet duration vanishes: $d{\tau }_{\mathrm{pulse}}\left(L_c\right)/dz=0$.

Figure 3

The length $L_c$ at which the derivative of the laser pulse duration with respect to the evolution coordinate $z$ vanishes $[d{\tau }_{\mathrm{pulse}}\left(L_c\right)/dz=0\text{]}$ as a function of the initial amplitude in the laser pulse and the plasma density. Here, the amplitude is set in dimensionless units and the length in dimensional units.

Figure 4

Dynamics of laser pulse intensity at the plasma wake wave excitation in a gas jet 55 mm long, where $n_e=2\times {10}^{18}{\mathrm{cm}}^{-3}$ is plasma concentration. Initial parameters of the laser pulse: ${\tau }_p^{\mathrm{in}}=30$ fs is the initial duration of the laser pulse, $r_0=50\mu \mathrm{m}$ is the beam size, $P=13$ PW is the power, $({\omega }_p/{\omega }_0{)}^2=0.0015$, and ${\tau }_p^{\mathrm{out}}=3.5$ fs is the duration of the compressed laser pulse (at $z=0.52$ cm).